Having function v(x,a) - velocity for simple harmonic movement - as described below:
If I do the summation like this:
The result is 31.97. I would expect it as
32 instead. Why I still get the approximated result? If I keep increasing the
a parameter the summation becomes more and more away from
I realized I didn't give too much context of what I am trying to achieve, so here it is:
I am trying to simulate a simple harmonic movement (a platform going up and down, repeatedly), so I thought would be a good idea to use sine/cosine functions to go about this.
So my constraint for a graph of Position x Frames (time) would look like this:
As you can see, the maximum amplitude point of this wave is between 32 and -32.
But I simply cannot assign the position directly (limitations of the program I am using), instead, I have to set the velocity. The velocity is always 60x the position. That means if I assign 1 to the velocity during 1 frame, the displacement will be
1/60 = 0.01666666666666667. 60 is the number of frames per second.
So the first function
v(x, a) was my first attempt to make sure, after N cycles the maximum displacement would be always 32. So I don't know what function I should use to have a result displacement (summation) of 32.
I hope I made my question a bit more clear, thanks for relentless help.